Normal Integration: A Survey

TL;DR

This survey reviews existing normal integration methods in computer vision, analyzing their properties and limitations, and highlights the need for methods that are accurate, fast, robust, and capable of handling complex boundary conditions and depth discontinuities.

Contribution

It provides a comprehensive analysis of normal integration methods based on key properties and identifies gaps, guiding future research in developing more effective algorithms.

Findings

No existing method satisfies all desired properties

Most methods struggle with depth discontinuities and boundary conditions

The survey highlights the need for improved normal integration techniques

Abstract

The need for efficient normal integration methods is driven by several computer vision tasks such as shape-from-shading, photometric stereo, deflectometry, etc. In the first part of this survey, we select the most important properties that one may expect from a normal integration method, based on a thorough study of two pioneering works by Horn and Brooks [28] and by Frankot and Chellappa [19]. Apart from accuracy, an integration method should at least be fast and robust to a noisy normal field. In addition, it should be able to handle several types of boundary condition, including the case of a free boundary, and a reconstruction domain of any shape i.e., which is not necessarily rectangular. It is also much appreciated that a minimum number of parameters have to be tuned, or even no parameter at all. Finally, it should preserve the depth discontinuities. In the second part of this survey, we review most of the existing methods in view of this analysis, and conclude that none of them satisfies all of the required properties. This work is complemented by a companion paper entitled Variational Methods for Normal Integration, in which we focus on the problem of normal integration in the presence of depth discontinuities, a problem which occurs as soon as there are occlusions.